The invention described herein may be manufactured and used by or for the US Government for governmental purposes without the payment of any royalty thereon.
1. Background-Field of the Invention
The present invention relates to improving the detection performance of multi-channel receivers, and, in particular, to improving the detection of signals masked by the presence of partially correlated Gaussian or non-Gaussian noise plus additive Gaussian thermal white noise. The apparatus and method of the present invention is directed to the signal processing architecture and computational procedures of multi-channel receivers. The present invention has radar, sonar, geophysical, and biomedical applications.
2. Background-Description of the Prior Art
The use of multi-channel signal processing methods to detect the presence of a desired signal is well established. Basing such methods on parametric models offers the prospect of improved performance over the prior art.
In airborne array radar applications, for example, with J antenna elements (spatial channels) and N pulses per coherent processing interval (xe2x80x9cCPIxe2x80x9d), optimal signal detection methods using both angle- and Doppler-processing require joint space-time matched filtering in the JNxc3x97JN complex vector space. Such techniques are generally computationally prohibitive, and they require large amounts of secondary data (i.e., data from the radar surveillance region assumed to be free of the target signal of interest) to estimate the noise disturbance correlation. In addition, for conditions of non-homogeneous clutter, the secondary data may lack statistical equivalence to that in the range cell under test. Also, for the conventional Gaussian receiver, distinct thresholds must be established for individual range-azimuth cells over the entire radar surveillance volume. This requirement follows from the observation that the data sequence of N pulses is Gaussian for each individual range cell but non-Gaussian from cell to cell.
The performance of Gaussian receivers is improved to a degree by the systems described in the following U.S. patents:
U.S. Pat. No. 5,640,429 issued to Michels and Rangaswamy
U.S. Pat. No. 5,272,698 issued to Champion
U.S. Pat. No. 5,168,215 issued to Puzzo
U.S. Pat. No. 4,855,932 issued to Cangiani
U.S. Pat. No. 6,226,321 issued to Michels, et. al.
Cangiani et al. discloses a three dimensional electro-optical tracker with a Kalman filter in which the target is modeled in space as the superposition of two Gaussian ellipsoids projected onto an image plane. Puzzo offers a similar disclosure. Champion discloses a digital communication system.
Michels et al., U.S. Pat. No. 6,226,321, hereby incorporated by reference, discloses implementations, for a signal that has unknown amplitude. For the signal of unknown amplitude, Michels et al. teaches how to incorporate the estimated signal amplitude directly into the parametric detection procedure. Furthermore, Michels teaches two separate methods, namely, (1) how to detect the signal in the presence of partially correlated non-Gaussian clutter disturbance and (2) how to detect the signal in the presence of partially correlated Gaussian clutter disturbance. Furthermore, the method to detect the signal in the presence of partially correlated non-Gaussian clutter involves processing the received radar data and requires the use of functional forms that depend upon the probability density function (pdf) of the disturbance. Thus, the latter method requires knowledge of the pdf statistics of the non-Gaussian disturbance. The method does not teach how to process the data in such a manner that would not require knowledge of the disturbance process. Furthermore, it does not teach how to process the data with one method that would detect the signal in either Gaussian or non-Gaussian disturbance. Thus there exists a need for apparatus and method of processing the data with a detection method that does not require knowledge of the clutter statistics. Furthermore, there exists a need for a method that detects the signal in either Gaussian or non-Gaussian disturbance.
The performance improvements of the presently disclosed invention relative to prior art are detailed in J. H. Michels, M. Rangaswamy, and B. Himed, xe2x80x9cEvaluation of the Normalized Parametric Adaptive Matched Filter STAP Test in Airborne Radar Clutter,xe2x80x9d IEEE International Radar 2000 Conference, May 7-11, 2000, Washington, D.C. and J. H. Michels, M. Rangaswamy, and B. Himed, xe2x80x9cPerformance of STAP Tests in Compound-Gaussian Clutter,xe2x80x9d First IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM 2000), Mar. 16-17, 2000, Cambridge, Mass. Both of these documents, designated references A and B, respectively, are incorporated herein by reference thereto.
Therefore one object of the present invention is to provide apparatus and method of detecting desired signals in additive Gaussian or non-Gaussian disturbance processes using single-channel or multiple-channel sensors.
Another of the present invention is to provide apparatus and method of detecting desired signals in additive Gaussian or non-Gaussian disturbance processes that use efficiently the available data from secondary data cells; i.e., require only a small number of secondary data cells.
Still another object of the present invention is to provide apparatus and method of detecting desired signals in additive Gaussian or non-Gaussian disturbance processes that uses linear prediction error filters.
Briefly stated, the present invention provides an apparatus and method for improving the detection of signals obscured by either correlated Gaussian or non-Gaussian noise plus additive jamming interference and thermal white Gaussian noise. Estimates from multi-channel data of model parameters that describe the noise disturbance correlation are obtained from data that contain signal-free data vectors, referred to as xe2x80x9csecondaryxe2x80x9d or xe2x80x9creferencexe2x80x9d cell data. These parameters form the coefficients of a multi-channel whitening filter. A data vector, referred to as the xe2x80x9ctest cellxe2x80x9d or xe2x80x9cprimaryxe2x80x9d data vector, to be tested for the presence of a signal passes through the multi-channel whitening filter. The filter""s output is then processed to form a test statistic. The test statistic is compared to a threshold value to decide whether a signal is xe2x80x9cpresentxe2x80x9d or xe2x80x9cabsentxe2x80x9d. Embodiments of the apparatus and method include estimating the signal amplitude both implicitly and explicitly and calculating test statistics for signal detection in both Gaussian and non-Gaussian noise.
According to an embodiment of the invention, in a system for processing signals, a method for identifying presence or absence of at least one potential target comprises the steps of: receiving from multiple channels signals corrupted by Gaussian or non-Gaussian disturbance; partitioning the signals into secondary data having a low probability of containing the potential target and primary data to be assessed for the presence of the target; estimating at least one linear filter parameter from the secondary data; filtering at least one steering vector and the primary data with at least one whitening filter based on the at least one linear filter parameter to produce at least one steering vector residual and at least one primary data residual; calculating a first test statistic as a function of the at least one linear filter parameter, the at least one steering vector residual, and the at least one primary data residual; and comparing the first test statistic to a threshold value to provide a xe2x80x9ctarget presentxe2x80x9d or a xe2x80x9ctarget absentxe2x80x9d response when the signals are corrupted by Gaussian disturbance.
According to a feature of the invention, in a system for processing signals, a method for identifying presence or absence of at least one potential target comprises the steps of: receiving from multiple channels signals corrupted by Gaussian or non-Gaussian disturbance; partitioning the signals into secondary data having a low probability of containing the potential target and primary data to be assessed for the presence of the target; estimating at least one linear filter parameter from the secondary data; filtering at least one steering vector and the primary data with at least one whitening filter based on the at least one linear filter parameter to produce at least one steering vector residual and at least one primary data residual; estimating signal amplitude as a function of the at least one linear filter parameter, the at least one steering vector residual, and the at least one primary data residual, thereby obtaining an estimated signal amplitude; multiplying the at least one steering vector residual by the estimated signal amplitude to obtain a scaled steering vector residual; subtracting the scaled steering vector residual from the at least one primary data residual to create an intermediate result; calculating a first quadratic term as a function of the at least one primary data residual and the at least one linear filter parameter; calculating a second quadratic term as a function of the intermediate result and the at least one linear filter parameter; subtracting the second quadratic term from the first quadratic term to form a first test statistic; and comparing the first test statistic to a threshold value to provide a xe2x80x9ctarget presentxe2x80x9d or a xe2x80x9ctarget absentxe2x80x9d response when the signals are corrupted by Gaussian disturbance.
According to another feature of the invention, apparatus for processing signals from which to identify presence or absence of at least one potential target, comprises: means for receiving multi-channel signals containing the at least one potential target obscured by Gaussian or non-Gaussian disturbance; means for partitioning the signals into secondary data having a low probability of containing the potential target and primary data to be assessed for the presence of the potential target; means for estimating at least one linear filter parameter from the secondary data; means for filtering at least one steering vector and the primary data with at least one whitening filter based on the at least one linear filter parameter to produce at least one steering vector residual and one primary data residual; first calculating means for calculating a first test statistic as a function of the at least one linear filter parameter, the steering vector residual, and the primary data residual; and means for comparing effective for comparing the first test statistic to a threshold value to provide a xe2x80x9ctarget presentxe2x80x9d or a xe2x80x9ctarget absentxe2x80x9d response when the signals are corrupted by Gaussian disturbance.
According to still another feature of the invention, apparatus for processing signals from which to identify presence or absence of at least one potential target, comprises: means for receiving multi-channel signals containing the potential target obscured by Gaussian or non-Gaussian disturbance; means for partitioning the signals into secondary data having a low probability of containing the potential target and primary data to be assessed for the presence of the potential target; means for estimating at least one linear filter parameter from the secondary data; means for filtering at least one steering vector and the primary data with at least one whitening filter based on the at least one linear filter parameter to produce at least one steering vector residual and one primary data residual; first calculating means for calculating an estimate of signal amplitude as a function of the at least one linear filter parameter, the steering vector residual, and the primary data residual; means for multiplying the filtered steering vector residual by the estimate of signal amplitude to create a scaled steering vector residual; first subtracting means for subtracting the scaled steering vector residual from the primary data residual to create an intermediate result; second calculating means for calculating a first quadratic term as a function of the primary data residual and the at least one linear filter parameter; third calculating means for calculating a second quadratic term as a function of the intermediate result and the at least one linear filter parameter; second subtracting means for subtracting the second quadratic term from the first quadratic term to form a first test statistic; and means for comparing the first test statistic to a threshold value to provide a xe2x80x9ctarget presentxe2x80x9d or a xe2x80x9ctarget absentxe2x80x9d response when the signals are corrupted by Gaussian disturbance.
The apparatus and method of the present invention provide a multi-channel receiver that improves the detection of target signals in the presence of either Gaussian or non-Gaussian correlated clutter together with additive jamming interference and thermal white noise. Further, the present invention provides such improved target detection without requiring knowledge of the clutter statistics. The present invention improves detection for radar, sonar, biomedical diagnostics, geophysical data processing, etc., where the input data contain either Gaussian or non-Gaussian disturbance. This improvement is achieved through the signal processing architecture and computational procedure described below.
Several important features of the present invention are: (1) it can process both single and multiple channel data; (2) the implementation described below applies to the detection of a signal with unknown amplitude embedded in disturbances of unknown correlation; (3) the detection architecture is canonical for non-Gaussian clutter described by spherically invariant random processes (xe2x80x9cSIRPsxe2x80x9d) (Rangaswamy, M., et. al., xe2x80x9cComputer generation of correlated non-Gaussian radar clutter,xe2x80x9d IEEE Trans. on Aerospace and Electronic Systems, vol. AES-31, pp. 106-116, 1995), i.e., the circuitry does not change when the statistics of the input data processes change; (4) the minimum mean squared error (MMSE) parameter estimators in the present invention are linear for the large class of non-Gaussian SIRPs that comprise the disturbance; (5) the implementation described below for the K (.alpha.=0.5)-receiver offers robust performance for a wide range of non-Gaussian as well as Gaussian noise, where .alpha. is the shape parameter of the clutter probability density function (xe2x80x9cpdfxe2x80x9d).
In the present invention, the unknown disturbance correlation is estimated from secondary data by means of parametric adaptive estimation algorithms. However, the estimate of signal amplitude is now embedded directly into the detection test statistic. Thus a large covariance matrix requiring approximately 2 JN range cells is no longer required, with the result that high detection performance can be achieved with a very low number of range cells.
In a preferred embodiment of the present invention for the detection of moving objects from an airborne radar, the processing system uses baseband sensor data from the A/D converters of an airborne phased array radar. This sensor data is organized as a J.times.1 vector sequence, where each element of the vector corresponds to a particular array element (or column), and each index in the sequence corresponds to a time sample that relates to a specific transmitted pulse of the N pulse coherent processing interval (xe2x80x9cCPIxe2x80x9d). A third dimension of the data is obtained from the K range rings measured from the radar. These range rings are swept by each pulse, thus providing K with Jxc3x971 observation data vectors in fast time for each of the N pulses in slow time. Thus, the data can be stacked in a data cube of dimension Jxc3x97Nxc3x97K.
To determine the presence or absence of a target, data are chosen from a specific range cell, the xe2x80x9ctest cellxe2x80x9d. Data from range cells immediately surrounding the test cell are xe2x80x9cguard bandxe2x80x9d cell data. Several procedures can determine the disturbance""s (e.g., ground clutter, jamming interference, thermal white noise) correlation properties. In one procedure, both the test cell and guard band data are removed from the data cube, leaving the xe2x80x9csecondaryxe2x80x9d or xe2x80x9creferencexe2x80x9d cell vectors, which are assumed to be signal free. In an alternative procedure, no vectors are removed from the data cube.
Linear parametric models (xe2x80x9cLPMsxe2x80x9d) describe the noise disturbance correlation. There are two general classes of such models for vector random processes: time series and state space. Either kind of LPMs falls within the intended scope of the present invention. Any of several multi-channel algorithms can estimate the parameters of the respective model types. The multichannel least squares (MLS) algorithm (S. L. Marple, Digital Spectral Analysis, Prentice Hall, 1987), Nuttall-Strand (Nuttall, A. H., xe2x80x9cMultivariate linear predictive spectral analysis employing weighted forward and backward averaging: A generalization of Burg""s algorithm,xe2x80x9d Naval Underwater Systems Center TR-5501, New London, Conn. October 1976; Strand, O. N., xe2x80x9cMulti-channel complex maximum entropy (auto-regressive) spectral analysis,xe2x80x9d IEEE Trans. Antom. Control, vol, AC-22, pg 634-640, August 1977) and Vierra-Morf (Morf, M., Vierra, A., Lee, D., Kailath, T., xe2x80x9cRecursive Multi-channel maximum entropy spectral estimation,xe2x80x9d IEEE Trans. on Geoscience Electronic, vol GE-16, no 2, April 1978) are algorithms that apply to time series models. A number of recently-developed multi-channel state space algorithms (Roman, J., Davis, D., xe2x80x9cMulti-channel Parametric Models for Airborne Radar Array Clutter,xe2x80x9d 1997 IEEE National Radar Conference, Syracuse, N.Y., May 13-15, 1997) apply to state space models. The model parameters estimated from any candidate algorithm form the coefficients in a multi-channel whitening filter. Both the data vector from the test cell and the known steering vector written in time sequential form are passed through this filter. The output vectors from the multi-channel whitening filter are then processed to form a scalar xe2x80x9ctest statistic.xe2x80x9d The xe2x80x9ctest statisticxe2x80x9d is then compared to a threshold value to decide whether a signal is present or absent.
The following definitions serve to clarify the present invention:
A/D Converter: a device that converts analog signals to digital signals.
Adaptive Matched Filter: a matched filter detector in which the disturbance covariance matrix is replaced with its estimate.
Clutter Shape Parameter (a): is the parameter that changes the K-distribution for clutter from Gaussian (xcex1="igr"xcexdxcfx86) to a high tailed probability density function (xcex1=0.1). Coefficients of Linear Prediction: the coefficients that weight a linear combination of time series of past data from a given process to estimate the process at some point in time.
Coherent Processing Interval (CPI): the number of pulses generated by a radar in an interval of time over which the radar maintains phase coherence.
Constant False Alarm Rate (CFAR): attribute of a receiver that maintains the false alarm rate fixed in the presence of changing interference levels.
Data Cube: the organization of data consisting of various channels, range cells, and pulses into a three-dimensional configuration for storage.
Diagonal Matrix: a matrix with whose elements are non-zero only along the diagonal.
Diagonal Matrix Coefficient (D): obtained from the LDL decomposition of either the model residual covariance matrix or the sample residual covariance matrix estimates.
Disturbance: all unwanted noise that interferes with the desired signal.
False Alarm: the decision that a signal is present when in fact it is not.
Fast Time: the round-trip time delay, as measured between range cells, of a single radar pulse (which travels at the speed of light).
Guard Band: the data, collected from range rings adjacent to the test cell, which are eliminated from the secondary data cells before estimating the disturbance statistics.
Host System: the system supported by the present invention.
Input Signal-to-Interference plus Noise Ratio: the ratio of the filter input signal power to the input power of the interference and white noise.
Linear Filter Parameters: the estimated coefficients of linear prediction used in the whitening filter of the parametric adaptive matched filter.
Matched Filter: in the context of this application, a linear filter that maximizes the output signal-to-interference-plus-noise ratio.
Model Residual Covariance: the estimated error covariance matrix obtained from a parameter estimation algorithm such as Nuttall-Strand.
Output Signal-to-Interference plus Noise Ratio: the ratio of the filter output signal power to the output power of the interference and white noise.
Prediction Error Filter: a filter that provides the difference operation between the input signal and its estimate formed by the weighted sum of past data values.
Range Rings: the concentric lines of constant range measured from the radar location, each with a width related to the radar bandwidth.
Reference Cell Data: data collected from range rings assumed to be free of the desired signal (also called secondary data).
Sample Covariance Matrix: the estimator of the covariance of a data vector process obtained from the mean of the outer products of the multiple realizations of the data vector.
Sample Residual Covariance: the estimated error covariance matrix obtained by applying the sample covariance matrix estimator to the prediction error filter output data.
Secondary Data: data collected from range rings assumed to be free of the desired signal.
Signal to Interference plus Noise Ratio (SINR): is the ratio of target signal power (or amplitude) to the sum of interference and noise power (or amplitude).
Slow Time: the interval between successive pulses from the radar.
Spherically Invariant Random Process: results from the modulation of a Gaussian process by a statistically independent random variable.
Signal Steering Vector: contains the bearing and Doppler information associated with a radar signal.
Test Cell Data: contained in the radar range cell under test for the presence or absence of a radar signal.
Test Statistic: a scalar quantity, computed from received radar data and compared to a pre-determined threshold value to determine the presence or absence of a radar signal.
Threshold: a scalar quantity compared to a test statistic to determine the presence or absence of a desired signal and chosen to maintain a specific criterion, such as the cost associated with correct and incorrect decisions or the specification of the probability of a false alarm.
Time Sequential Form: in the context of the present invention, the formatting of a signal or data vector as a time series.
Whitening Filter: transforms the correlated input data to uncorrelated white noise.
Zero Memory Non-linear Transform: method of transforming blocks of data to maintain dependence between the individual blocks.
The above and many other objects and advantages of the present invention will be readily apparent to one skilled in the pertinent art from the following detailed description of preferred embodiments of the invention and the related drawings, in which like reference numerals designate the same elements.